, Volume 34, Issue 4, pp 489–507 | Cite as

Estimation of true score and error variance for tests under various equivalence assumptions

  • Walter Kristof


Maximum-likelihood estimators of true score variance and error variance for mental tests are derived for six different models of equivalent measurements. Statistical properties of the estimators are examined. Main emphasis is placed upon essentiallyτ-equivalent measurements. A statistical criterion for this type of measurement is given. The solution of the comparatively simple maximum-likelihood equations is effected by means of a rapid Newton-Raphson procedure. Two different initial estimators are considered and their relative merits in terms of second moments evaluated. Four numerical examples are appended by way of illustration.


Public Policy Statistical Criterion Statistical Theory Error Variance Relative Merit 
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  1. Anderson, T. W.Introduction to multivariate statistical analysis. New York: Wiley, 1958.Google Scholar
  2. Gulliksen, H.Theory of mental tests. New York: Wiley, 1950.Google Scholar
  3. Jöreskog, K. G. Statistical models for congeneric test scores.Proceedings, 76th Annual Convention, APA, 1968, 213–214.Google Scholar
  4. Kristof, W. Statistical inferences about the error variance.Psychometrika, 1963,28, 129–143. (a)Google Scholar
  5. Kristof, W. The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts.Psychometrika, 1963,28, 221–238. (b)Google Scholar
  6. Lord, F. M., & Novick, M. R.Statistical theories of mental test scores. Reading, Mass.: Addison-Wesley, 1968.Google Scholar
  7. Novick, M. R., & Lewis, C. Coefficient alpha and the reliability of composite measurements.Psychometrika, 1967,32, 1–13.Google Scholar
  8. Wilks, S. S. Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution.Annals of Mathematical Statistics, 1946,17, 257–281.Google Scholar

Copyright information

© Psychometric Society 1969

Authors and Affiliations

  • Walter Kristof
    • 1
  1. 1.Educational Testing ServiceUSA

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